Diff. Geom, Math. Phys., PDE Seminar: Hyunju Kwon

We consider the Cauchy problem of 3D incompressible Navier-Stokes equations for uniformly locally square integrable initial data. The existence of a time-global weak solution has been known, when the square integral of the initial datum on a ball vanishes as the ball goes to infinity. For non-decaying data, however, the only known global solutions are either for perturbations of constants or when the velocity gradients are in Lp with finite p. In this talk, I will outline how to construct global weak solutions for general non-decaying initial data whose local oscillations slowly decay.
This is a joint work with Tai-Peng Tsai.